Abstract
This paper introduces a new statistical distribution called the Neutrosophic Extended Rayleigh Distribution (NERD), which is specifically developed to handle uncertainty commonly found in industrial applications. We conduct a comprehensive examination of the statistical characteristics of NERD, including important measures such as the quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, uncertainty measures, distributions of order statistics, and L-moments. Parameter estimation is conducted by maximum-likelihood estimation within a neutrosophic framework, guaranteeing resilient inference in practical situations. Through the application of NERD to actual industrial datasets, we evaluate its adaptability and efficiency in simulating industrial processes. A real case study of Al-Kharj region demonstrates the higher performance of NERD. This research highlights the capacity of NERD to greatly improve productivity and efficiency in several industrial sectors.
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